Laparoscopic surgical training poses significant skill acquisition challenges, which can be overcome through automated skill assessments and objective feedback mechanisms. Such analysis fundamentally depends on accurate 3D pose estimation of instruments. Existing approaches rely on bulky hardware, additional markers, prior 3D models, or multi-view camera setups. In contrast, our work proposes and evaluates a deep learning-enabled modular pipeline for markerless 3D pose estimation of instruments from a single camera. In this paper we conduct a comprehensive evaluation of both the deep learning detection module and the pipeline's 3D pose estimation performance under unseen and challenging conditions representative of realistic simulator scenarios. The detection model achieves an mAP0.5-0.95 of 99.3% on the test set, and the pipeline demonstrates mean absolute errors (MAE) of 1.53 mm, 1.44 mm, and 1.50 mm along the X, Y and Z axes respectively. Our findings indicate that the proposed pipeline generalizes robustly to realistic simulator conditions, thereby advancing the feasibility of automated skill assessment and practical deployment in laparoscopic training environments, ultimately contributing to improved quality of surgical training and patient outcomes.